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Volume of solids
Tvrdá, Monika ; Halas, Zdeněk (advisor) ; Staněk, Jakub (referee)
This didactic oriented bachelor project helps to approach an origin of relations for the volumes of solids taught at high school. It is focused on high school and university students. At the beginning the project shows historical meaning of the volumes of solids and the processes which were used to enumerate them in the ancient Egypt and Mesopotamia. Further, the project deals with the definition of volume of solids; it is based on Jordan's measure. The relations for volumes of the sorted solids are derived using the integral calculus. In the end the other ways of deriving of these relations are shown. At first, it is the method that Archimedes from Syracuse invented, furthermore by the visual imaginations and the Cavalieri's principle. 1
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History of PI
Bernátová, Eliška ; Kvasz, Ladislav (advisor) ; Pilous, Derek (referee)
My bachelor thesis "History of " aims to inform about the development of this constant. I tried to proceed chronologically from the beginnings in ancient Egypt through ancient Greece, the Middle Ages, the Renaissance to the Modern Era and the computer's world. In the chapters "The Mysterious Middle Ages" and " the Hunting of the Precise Numbers" are focused mainly on the most important personalities of the time. Of course, the problem of was dealt with a countless number of mathematicians, but to mention each any of them would take a lot of time and the thesis would have hundreds of pages. After due consideration I selected the most interesting personalities, those whose contribution to the development of deserved it most. In the next chapter, "Irrationality and Transcendence" I primarily focused on mathematical theorems and their proofs. This chapter is the most important in my opinion. Many circumstances related to the number are resolved there in. In the final chapter, which I called " in the Computer World" I mention only the most important computers until 1967 because of the very rapid development of technology after wards.
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Platonic and Archimedean solids and their properties in teaching of mathematics at secondary schools
Dohnalová, Eva ; Robová, Jarmila (advisor) ; Halas, Zdeněk (referee)
Title: Platonic and Archimedean solids and their properties in teaching of mathematics at secondary schools Author: Eva Dohnalová Department: Department of Didactics of Mathematics Supervisor: doc. RNDr. Jarmila Robová, CSc. Abstract: This work is an extension of my bachelor work and it is intended for all people interested in regular and semiregular polyhedra geometry. It is a comprehensive text which summarizes brief history, description and classification of regular and semiregular polyhedra. The work contains proofs of Descartes' and Euler's theorems and proofs about number of regular and semiregular polyhedra. It can be also used as a didactic aid in the instruction of regular and semiregular solids at secondary schools. This text is supplemented by illustrative pictures made in GeoGebra and Cabri3D. Keywords: Regular polyhedra, platonic solids, Platon, semiregular polyhedra, Archimedean solids, Archimedes, dulaism, Descartes' theorem, Euler's theorem.
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The number π and continued fractions
Švejdová, Aneta ; Halas, Zdeněk (advisor) ; Slavík, Antonín (referee)
This bachelor thesis deals with one of the well-known mathematical constants, the number π. The form is understandable to higher-year students of secondary schools interested in mathematics. At first, it presents the best known ways people in history tried to approximate the number π. It includes the methods of Egyptians, the people of ancient Mesopotamia and the method of Archimedes. It also presents expressing π in the form of infinite product according to F. Viète and J. Wallis. The second part of the thesis focuses on expressing the number π by continued fractions, which are at first generally defined. We introduce essential relations among them. Then the thesis presents expressing the number π in the form of continued fractions according to J. H. Lambert, L. Euler and W. Brouncker. Finally, proofs of the irrationality of π using continued fractions are presented together with a simple proof of its transcendence. The aim of the thesis is to extend information about π stated in popular books, to explain and clarify basic ideas leading to these claims.
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Platonic and Archimedean solids and their properties in teaching of mathematics at secondary schools
Dohnalová, Eva ; Robová, Jarmila (advisor) ; Halas, Zdeněk (referee)
Title: Platonic and Archimedean solids and their properties in teaching of mathematics at secondary schools Author: Eva Dohnalová Department: Department of Didactics of Mathematics Supervisor: doc. RNDr. Jarmila Robová, CSc. Abstract: This work is an extension of my bachelor work and it is intended for all people interested in regular and semiregular polyhedra geometry. It is a comprehensive text which summarizes brief history, description and classification of regular and semiregular polyhedra. The work contains proofs of Descartes' and Euler's theorems and proofs about number of regular and semiregular polyhedra. It can be also used as a didactic aid in the instruction of regular and semiregular solids at secondary schools. This text is supplemented by illustrative pictures made in GeoGebra and Cabri3D. Keywords: Regular polyhedra, platonic solids, Platon, semiregular polyhedra, Archimedean solids, Archimedes, dulaism, Descartes' theorem, Euler's theorem.
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History of PI
Bernátová, Eliška ; Kvasz, Ladislav (advisor) ; Pilous, Derek (referee)
My bachelor thesis "History of " aims to inform about the development of this constant. I tried to proceed chronologically from the beginnings in ancient Egypt through ancient Greece, the Middle Ages, the Renaissance to the Modern Era and the computer's world. In the chapters "The Mysterious Middle Ages" and " the Hunting of the Precise Numbers" are focused mainly on the most important personalities of the time. Of course, the problem of was dealt with a countless number of mathematicians, but to mention each any of them would take a lot of time and the thesis would have hundreds of pages. After due consideration I selected the most interesting personalities, those whose contribution to the development of deserved it most. In the next chapter, "Irrationality and Transcendence" I primarily focused on mathematical theorems and their proofs. This chapter is the most important in my opinion. Many circumstances related to the number are resolved there in. In the final chapter, which I called " in the Computer World" I mention only the most important computers until 1967 because of the very rapid development of technology after wards.
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Volume of solids
Tvrdá, Monika ; Halas, Zdeněk (advisor) ; Staněk, Jakub (referee)
This didactic oriented bachelor project helps to approach an origin of relations for the volumes of solids taught at high school. It is focused on high school and university students. At the beginning the project shows historical meaning of the volumes of solids and the processes which were used to enumerate them in the ancient Egypt and Mesopotamia. Further, the project deals with the definition of volume of solids; it is based on Jordan's measure. The relations for volumes of the sorted solids are derived using the integral calculus. In the end the other ways of deriving of these relations are shown. At first, it is the method that Archimedes from Syracuse invented, furthermore by the visual imaginations and the Cavalieri's principle. 1
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